For example, if you adjusted the music with auto gain / keyframes and you have to cut out something in the beginning, you have to move every single keyframe which is not very effective.

why can't I select in and out, press alt and move all keyframes horizontally ? That's how you can move them vertically (without alt) but not horizontally. 

You just have to move them one at a time (with alt). What could be the problem with that?

:-)